10 papers · 1 filter
Binary Multiple-Node-Erasure-Correcting Codes over Complete Graphs: Constructions, q-Ary Metric Balls, and Duality
Aryeh Lev Zabokritskiy
We study linear codes whose coordinates are the ordinary edges and self-loops of complete undirected graphs; a node erasure removes all coordinates incident with a failed vertex. T…
Coding for Multiple Reverse-Complement and Palindromic Duplications
Aryeh Lev Zabokritskiy
Reverse-complement (RC) and palindromic (PAL) duplications copy a length- block, reverse the copy, and insert it immediately after the original block; an RC duplication also com…
Quantitative tiling stability from quadratic discrepancy in Hamming spaces
Valery, Grishin, Aryeh Lev Zabokritskiy
Quadratic ball discrepancy defines an energy on codes in finite Hamming spaces. At perfect-code parameters, its exact minimizers are the perfect codes. We fix the alphabet size, le…
Asymptotically Tight Bounds for Generalized Covering Radii of Binary Primitive BCH Codes at All Higher Orders
Zeev Vladimir Belinsky, Aryeh Lev Zabokritskiy
We study how few parity-check columns are needed to span several prescribed syndromes of a binary primitive BCH code of length , where is the extension degree. For the f…
The Exact Second Generalized Covering Radius of Binary Primitive Triple-Error-Correcting BCH Codes
Isaac Barouch Essayag, Aryeh Lev Zabokritskiy
Let be the binary primitive triple-error-correcting BCH code of length . We determine its second generalized covering radius exactly: $R_2(C_m)…
Perfect codes as exact minimizers of quadratic discrepancy in q-ary Hamming spaces
Aryeh Lev Zabokritskiy
Stolarsky's invariance principle converts quadratic discrepancy into an energy-minimization problem. Barg developed its form for binary Hamming space and proved that binary perfect…